1. (Section 17.4) Use Green's Theorem to evaluate the line integral sir sin(y) dx + x dy, where C is the triangular path consisting of the line segment from (0,0) to (E, 0) followed by the line segment from (5,0) to (5, 5) followed by the line segment from (5,5) to (0,0). 2 2

Q: Q2) a) Find Maclaurin expression of f (x) = Cosh (x) b)Find the gradient of the function f(x, y, z)…

A: Part (a) General form of function fx is Maclaurin series is…

Q: Show that the directiona f(x, y, z) = z²x + y ² at ( X (1/15" + ) ; 255. them

A: fx,y,z=z2x+y3 P1,1,2v→=15i+25j We know directional derivative Dv→fP=∇fP.v→v→

Q: Let  f(x, y) = sin(15x2 + 3y2) Calculate the quadratic approximation of f at the point (0,0)

A: Given that,  fx, y=sin15x2+3y2 The quadratic approximation of the function fx, y at the point x0, y0…

Q: Find the points where the tangent is parallel to y=0. y=x*-8x°+22x2-24x+9 O E 0 (1,1),(2,2),(3,0) O…

A: Given: y=x4-8x3+22x2-24x+9 And y=0, represents the x-axis. The Power law: ddxxn=nxn-1

Q: (b) Verify that the following function is harmonic u(x, y) = −e sin x - 2e-siny. Find a harmonic…

A: Here we have to verify that the function is harmonic and then find the harmonic conjugate.

Q: Use Green's Theorem to evaluate the line integral along the given positively oriented curve. | yex…

A: To evaluate the given line integral along the given positively oriented curve. ∫Cyexdx+2exdy Where C…

Q: The maximum directional derivative of f(z,y,2) sin(zy)-ya +10 at (-1, 2, 0) is Question 5

A:

Q: An analytic function of a complex variable z = x + iy is expressed as f(z) = u(x, y) + iv(x, y).…

A:

Q: 2. Determine the directional derivative of o(x, y, z) = re" + y² + xyz at the point (2, 0, 3) in the…

A:

Q: 8. Find the directional derivative off at the p in the direction of v = () of f(x, y, z)=x²exx, p =…

A:

Q: 1) Find the linearization L(x) of f(x) at x = a. f(x) = 2x2 + 4x - 1, a =

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: Plot the slope field of y=x+y using slopes m = -3, -2,-1,0, 1, 2. Sketch integral curves for…

A: First we plot the slope field and then plot the curve .

Q: Study the analytically of w = L_r(z) at the points z = 0, z = v2,z = -2i

A:

Q: Find the tangential and normal components.  r(t)=(t+1)i+2tj+t^ 2 × k     ,   t = 1

A: We'll answer the first question since the exact one wasn't specified. Please submit a new question…

Q: The area of the surface obtained by rotating the curve y = 1<xse about the line x = 32 is ** 12 (32…

A:

Q: 3. From results obtained in Secs. 21 and 23, determine where f'(z) exists and find its value when…

A:

Q: 2.) у" - Зу' — 2у %3D0 У (0) %3D0, у'(0) %3D 9 ,у" %3D0

A:

Q: QI\ Find Fourier transform for: A) f(t) = U(t)sin² (3t) C) f(t) = elct sinh(bt)

A: (A)Given the function f(t)=u(t)sin2⁡(3t).Rewriting, .We know that, .The Fourier transform of f(t) is…

Q: Find the sbe and equation of the TANGENT and NORMAL LINE to the curve Graph cach curve, Kormal, and…

A:

Q: 13 Find the linearizatian z=L(x.y) f the function 2=f(x.y) =4x²-y²42y at the point (x.y) = (3,2).…

A:

Q: (b) Determine all functions f=u+ iv that are analytic in the whole plane and has the property that…

A:

Q: Determine coefficients a and b such that p(x)=x^2+ax+b satisfies p(1)=6 and p′(1)=0

A: Since you have posted multiple question in this question which are nt interlinked so i have solved…

Q: 19.3. (a) Using the chain rule, find ðf/ðz* and df/dz in terms of partial derivatives with respect…

A: We use chain rule

Q: Given that F = (4y² +e") ï+ (xe" +8xy) j, calculate the line integral So F • dr exactly, where C is…

A:

Q: What is the equation of the tangent plane to the graph of 3x²+4y²-2²=3 at the point (1,1,2) ? 03 1…

A:

Q: For which z values of the complex functions given below have the derivative (f'(z)), obtain a) f(z)…

A: The derivative of A function f at z=z0 is defined as  If f is polynomial in z , then f is…

Q: x = s·t u = x² + y³ +z*, {y = s² +² z = s- t

A:

Q: a) Find dy if y² + x²y² = 1+x^y use implicit differentiation b) If x² + y² = 6. Find y' in term OF…

A:

Q: Suppose F(x, y) = −y sin(x)i + cos(x)}. (a) Find a vector parametric equation for the parabola y =…

A:

Q: Verify that the given function u is harmonic in an appropriate domain D. Find its harmonic conjugate…

A:

Q: The direchional derivative of the salan funchion at (l,-1,0) in the direction (i-j+2k) is xy- z- xyz…

A: Given that  Let f(x,y,z)=x^2y-y^2z-xyz To find the directional derivative at point

Q: ) Find an analytic function f(z) = u(xr, y) + iv(r, y) with real part -. -----) u(r, y) = x? – y? +…

A: